2014-04-23 00:10:22 +00:00
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import numpy as np
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def comp_theta_mle(d):
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"""
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Computes the Maximum Likelihood Estimate for a given 1D training
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dataset for a Rayleigh distribution.
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"""
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2014-04-24 02:00:27 +00:00
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theta = len(d) / sum([x**2 for x in d])
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2014-04-23 00:10:22 +00:00
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return theta
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def likelihood_ray(x, theta):
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"""
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Computes the class-conditional probability for an univariate
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Rayleigh distribution
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"""
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return 2*theta*x*np.exp(-theta*(x**2))
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if __name__ == "__main__":
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training_data = [10, 18, 19, 22, 24, 29, 33, 40, 68]
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theta = comp_theta_mle(training_data)
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# Plot Probability Density Function
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from matplotlib import pyplot as plt
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x_range = np.arange(0, 20, 0.1)
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y_range = [likelihood_ray(theta, x) for x in x_range]
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plt.figure(figsize=(10,8))
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plt.plot(x_range, y_range, lw=2)
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plt.title('Probability density function for the Rayleigh distribution')
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plt.ylabel('p(x)')
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plt.xlabel('random variable x')
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plt.show()
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